Higher January 2020 Paper 2 Q20
20 The area of a rectangle is 18 cm²
The length of the rectangle is \(\left(\sqrt{7} + 1\right)\) cm.
Without using a calculator and showing each stage of your working,
find the width of the rectangle.
Give your answer in the form \(a\sqrt{b} + c\) where \(a\), \(b\) and \(c\) are integers.
(3)
| Scheme | Marks |
|---|---|
| \(\dfrac{18}{\sqrt{7} + 1} \times \dfrac{\sqrt{7} - 1}{\sqrt{7} - 1}\) | M1 |
| eg \(\dfrac{18(\sqrt{7} - 1)}{7 - 1}\) | M1 |
\(3\sqrt{7} - 3\) Working required Answer: \(3\sqrt{7} - 3\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for \(\dfrac{18}{\sqrt{7} + 1} \times \dfrac{\sqrt{7} - 1}{\sqrt{7} - 1}\)
M1: Dep on M1 for a correct numerator and multiplying out the denominator to 7 – 1 or 6
A1: Dep on M2
Allow \(3(\sqrt{7} - 1)\) (corrected from the printed mark scheme: the brackets are missing in the printed “Allow \(3\;\sqrt{7} - 1\)”)